<h2>题目编号 : 203</h2>
<div style="color:#666;font-size:80%;">06 September 2008</div><br />
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<p>The binomial coefficients <img src="" style="display:none;" alt="^(" /><sup>n</sup><img src="" style="display:none;" alt=")" />C<img src="" style="display:none;" alt="_(" /><sub>k</sub><img src="" style="display:none;" alt=")" /> can be arranged in triangular form, Pascal's triangle, like this:</p>

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<tr><td colspan="7"></td><td>1</td><td colspan="7"></td></tr>
<tr><td colspan="6"></td><td>1</td><td></td><td>1</td><td colspan="6"></td></tr>
<tr><td colspan="5"></td><td>1</td><td></td><td>2</td><td></td><td>1</td><td colspan="5"></td></tr>
<tr><td colspan="4"></td><td>1</td><td></td><td>3</td><td></td><td>3</td><td></td><td>1</td><td colspan="4"></td></tr>
<tr><td colspan="3"></td><td>1</td><td></td><td>4</td><td></td><td>6</td><td></td><td>4</td><td></td><td>1</td><td colspan="3"></td></tr>
<tr><td colspan="2"></td><td>1</td><td></td><td>5</td><td></td><td>10</td><td></td><td>10</td><td></td><td>5</td><td></td><td>1</td><td colspan="2"></td></tr>
<tr><td colspan="1"></td><td>1</td><td></td><td>6</td><td></td><td>15</td><td></td><td>20</td><td></td><td>15</td><td></td><td>6</td><td></td><td>1</td><td colspan="1"></td></tr>
<tr><td>1</td><td></td><td>7</td><td></td><td>21</td><td></td><td>35</td><td></td><td>35</td><td></td><td>21</td><td></td><td>7</td><td></td><td>1</td></tr>
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.........
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<p>It can be seen that the first eight rows of Pascal's triangle contain twelve distinct numbers: 1,&nbsp;2,&nbsp;3,&nbsp;4,&nbsp;5,&nbsp;6,&nbsp;7,&nbsp;10,&nbsp;15,&nbsp;20,&nbsp;21&nbsp;and&nbsp;35.</p>

<p>A positive integer <var>n</var> is called squarefree if no square of a prime divides <var>n</var>.
Of the twelve distinct numbers in the first eight rows of Pascal's triangle, all except 4 and 20 are squarefree.
The sum of the distinct squarefree numbers in the first eight rows is 105.</p>

<p>Find the sum of the distinct squarefree numbers in the first 51 rows of Pascal's triangle.</p>
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